Finite linear measurements in variational neural discretizations cause ill-posed discrete problems with non-unique minimizers, independent of the underlying continuous variational problem's well-posedness.
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An auxiliary finite-difference regularizer on residual gradients improves outer-wall flux and boundary-condition accuracy in a 3D annular heat-conduction PINN benchmark when aligned with the quantity of interest.
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Non-Uniqueness of Solutions in Neural Variational Methods
Finite linear measurements in variational neural discretizations cause ill-posed discrete problems with non-unique minimizers, independent of the underlying continuous variational problem's well-posedness.
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Auxiliary Finite-Difference Residual-Gradient Regularization for PINNs
An auxiliary finite-difference regularizer on residual gradients improves outer-wall flux and boundary-condition accuracy in a 3D annular heat-conduction PINN benchmark when aligned with the quantity of interest.